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In the field of quantum information science and technology, the representation and visualization of quantum states and related processes are essential for both research and education. In this context, a focus especially lies on ensembles of…
Qubits are a great way to build a quantum computer, but a limited way to program one. We replace the usual "states and gates" formalism with a "props and ops" (propositions and operators) model in which (a) the C*-algebra of observables…
We study separability criteria in multipartite quantum systems of arbitrary dimensions by using the Bloch representation of density matrices. We first derive the norms of the correlation tensors and obtain the necessary conditions for…
The two-qubit pure state is explicitly parameterized by three unit 2-spheres and a phase factor. For separable states, two of the three unit spheres are the Bloch spheres of each qubit. The third sphere parameterizes the degree and phase of…
We show that the covariance matrix of a quantum state can be reconstructed from position measurements using the simple notion of polar duality, familiar from convex geometry. In particular, all multidimensional Gaussian states (pure or…
Quantum information geometry studies families of quantum states by means of differential geometry. A new approach is followed with the intention to facilitate the introduction of a more general theory in subsequent work. To this purpose,…
In the design of quantum computing devices of the future the basic element is the qubit. It is a two-level quantum system which may describe population transfer from one steady-state to another controlled by a coherent laser field. A…
Poyiadjis et al. (2011) show how particle methods can be used to estimate both the score and the observed information matrix for state space models. These methods either suffer from a computational cost that is quadratic in the number of…
The discretization of the density matrix is proposed as a nonlinear positive map for systems with continuous variables. This procedure is used to calculate the entanglement between two modes through different criteria, such as Tsallis…
It is a hard and important problem to find the criterion of the set of positive-definite matrixes which can be written as reduced density operators of a multi-partite quantum state. This problem is closely related to the study of many-body…
We study quantum processes, as one parameter families of differentiable completely positive and trace preserving (CPTP) maps. Using different representations of the generator, and the Sylvester criterion for positive semi-definite matrices,…
We derive and analyze the perturbation series for the classical effective action in quantum statistical mechanics, treated as a toy model for the dimensionally reduced effective action in quantum field theory at finite temperature. The…
For a given discrete decomposable graphical model, we identify several alternative parametrizations, and construct the corresponding reference priors for suitable groupings of the parameters. Specifically, assuming that the cliques of the…
We present separability criteria for both bipartite and multipartite quantum states. These criteria include the criteria based on the correlation matrix and its generalized form as special cases. We show by detailed examples that our…
For a quantum state in a bipartite system represented as a density matrix, researchers used the realignment matrix and functions on its singular values to study the separability of the quantum state. We obtain bounds for elementary…
The most well-known tool for studying contextuality in quantum computation is the n-qubit stabilizer state tableau representation. We provide an extension that describes not only the quantum state, but is also outcome deterministic. The…
We express the matrix elements of the density matrix of the qutrit state in terms of probabilities associated with artificial qubit states. We show that the quantum statistics of qubit states and observables is formally equivalent to the…
We present three different matrix bases that can be used to decompose density matrices of d--dimensional quantum systems, so-called qudits: the generalized Gell-Mann matrix basis, the polarization operator basis, and the Weyl operator…
In this paper, a hybrid measurement and model-based method is proposed which can estimate the dynamic state Jacobian matrix in near real-time. The proposed method is computationally efficient and robust to the variation of network topology.…
In addition to the diagonalization of a normal matrix by a unitary similarity transformation, there are two other types of diagonalization procedures that sometimes arise in quantum theory applications -- the singular value decomposition…